Preparation: Preheat your oven to 375°F (190°C). Grease a 9×13-inch baking dish.

Cook the Beef: In a large skillet over medium heat, cook the ground beef and chopped onion until the beef is browned and the onion is translucent. Drain any excess fat.

Prepare the Sauce: In a medium-sized bowl, mix together the cream of mushroom soup, milk, sour cream, garlic powder, onion powder, salt, and pepper. Stir until smooth.

Layering: Begin by placing a layer of the thinly sliced potatoes at the bottom of the greased baking dish. Spread half of the beef and onion mixture over the potatoes. Pour half of the sauce mixture over the beef. Sprinkle half of the shredded cheddar cheese on top. Repeat the layers once more.

Baking: Cover the baking dish with aluminum foil and bake in the preheated oven for about 1 hour, or until the potatoes are tender.

Final Touches: Remove the foil and sprinkle the top with grated Parmesan cheese (if using). Return to the oven and bake for an additional 10-15 minutes, or until the top is golden brown and bubbly.

Serve: Remove from the oven and let it cool for a few minutes. Garnish with sliced green onions if desired. Serve warm.